Multigrid Methods for Saddle Point Problems: Darcy Systems
arXiv:1511.0832912 citations
Originality Synthesis-oriented
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Provides theoretical convergence guarantees for multigrid solvers applied to Darcy flow problems, which are important for porous media simulations.
The authors design and analyze multigrid methods for saddle point problems from mixed finite element discretizations of Darcy systems, proving uniform convergence of the W-cycle algorithm in a nonstandard energy norm.
We design and analyze multigrid methods for the saddle point problems resulting from Raviart-Thomas-Nédélec mixed finite element methods (of order at least 1) for the Darcy system in porous media flow. Uniform convergence of the $W$-cycle algorithm in a nonstandard energy norm is established. Extensions to general second order elliptic problems are also addressed.